Abstract

Previously, a quasi-steady form of the classical Rankine–Hugoniot weak
detonation has been shown to play an integral part in describing certain forms of
detonation initiation, arising during an intermediate stage between the thermal
ignition of the material and the first appearance of a strong detonation with
Zeldovich–von Neumann–D¨oring (ZND) structure. In this paper, we use a
parametric variable integration to calculate numerically the path of the weak
detonation in two important initiation scenarios, shock-induced and initial
disturbance-induced transition to detonation, via a large activation energy
induction domain model. The influence that the nature of the path may have on
the weak detonation structure is also discussed. In each case these calculations
enable us to predict how, where and when the transition to a strong detonation
with ZND structure will occur. Explanations for several phenomena observed
in both experiments and numerical studies on transition to detonation are also
uncovered by these calculations.